The data used can be spaced further in time by using the “neural ODE" approach developed by Chen et al. [1]}. In this approach a trajectory is evolved forward using a NN for \(f\)  with some numerical time integrator. Then the NN is trained to minimize the difference between this prediction and the true state. In Section  we outline this approach in more detail. The advantages this approach has over the other methods include data can be spaced further in time, trajectories can be evolved to arbitrary points in time, and adaptive time stepping can be used.
